Modelling and identification of non-linear deterministic systems in the delta-domain

This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta- domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure

Elastic Scattering of 6^6He based on a Cluster Description

Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is derived describing $^6$He in terms of a $^4$He-core and two neutrons. The Watson first order multiple scattering ansatz is extended to accommodate the internal dynamics of a composite cluster model for the $^6$He nucleus scattering from a nucleon projectile. The calculations are compared with the recent experiments at the projectile energy of 71 MeV/nucleon. In addition, differential cross sections and analyzing powers are calculated at selected higher energies.Comment: To be published in Phy. Rev.

QCD Sum Rules and Models for Generalized Parton Distributions

I use QCD sum rule ideas to construct models for generalized parton distributions. To this end, the perturbative parts of QCD sum rules for the pion and nucleon electromagnetic form factors are interpreted in terms of GPDs and two models are discussed. One of them takes the double Borel transform at adjusted value of the Borel parameter as a model for nonforward parton densities, and another is based on the local duality relation. Possible ways of improving these Ans{\"a}tze are briefly discussed.Comment: Contribution to the Festschrift on the occasion of Klaus Goeke's 60th birthday, to appear in Annalen der Physi

Conformal field theory approach to gapless 1D fermion systems and application to the edge excitations of nu = 1/(2p+1) quantum Hall sequences

We present a comprehensive study of the effective Conformal Field Theory (CFT) describing the low energy excitations of a gas of spinless interacting fermions on a circle in the gapless regime (Luttinger liquid). Functional techniques and modular transformation properties are used to compute all correlation functions in a finite size and at finite temperature. Forward scattering disorder is treated exactly. Laughlin experiments on charge transport in a Quantum Hall Fluid on a cylinder are reviewed within this CFT framework. Edge excitations above a given bulk excitation are described by a twisted version of the Luttinger effective theory. Luttinger CFTs corresponding to the nu =1/(2p+1) filling fractions appear to be rational CFTs (RCFT). Generators of the extended symmetry algebra are identified as edge fermions creators and annihilators, thus giving a physical meaning to the RCFT point of view on edge excitations of these sequences.Comment: 69 pages, 1 figure, LaTeX2e + amstex and graphicx packages needed, fullpage.sty used (not compulsory

First-principles derivation of the AdS/CFT Y-systems

We provide a first-principles, perturbative derivation of the AdS5/CFT4 Y-system that has been proposed to solve the spectrum problem of N=4 SYM. The proof relies on the computation of quantum effects in the fusion of some loop operators, namely the transfer matrices. More precisely we show that the leading quantum corrections in the fusion of transfer matrices induce the correct shifts of the spectral parameter in the T-system. As intermediate steps we study UV divergences in line operators up to first order and compute the fusion of line operators up to second order for the pure spinor string in AdS5xS5. We also argue that the derivation can be easily extended to other integrable models, some of which describe string theory on AdS4, AdS3 and AdS2 spacetimes.Comment: 45 pages, 5 figures; v2: minor additions, JHEP versio

Causal signal transmission by quantum fields. IV: The causal Wick theorem

Wick's theorem in the Schwinger-Perel-Keldysh closed-time-loop formalism is written in a form where the place of contractions is taken by the linear response function of the field. This result demonstrates that the physical information supplied by Wick's theorem for operators is propagation of the free field in space and time.Comment: Final version, to appear in Phys Rev

Looking for a theory of faster-than-light particles

Several principal aspects of a theoretical approach to the theory of faster-than-light particles (tachyons) are considered in this note. They concern the resolution of such problems of tachyon theory as the causality violation by tachyons, the stability of the tachyon vacuum, and the stability of ordinary particles against the spontaneous emission of tachyons, i.e. the problems which are generally used as arguments against the possibility of such particles. It is demonstrated that all these arguments contain nontrivial loopholes which undermine their validity. A demand for a consistent tachyon theory is formulated, and several ideas for its construction are suggested.Comment: 41 pages, 5 figure

From Quantum B\"acklund Transforms to Topological Quantum Field Theory

We derive the quantum analogue of a B\"acklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schr\"odinger equation. The quantisation of the Ablowitz-Ladik chain leads to the $q$-boson model. Using a previous construction of Baxter's Q-operator for this model by the author, a set of functional relations is obtained which matches the relations of a one-variable classical B\"acklund transform to all orders in $\hbar$. We construct also a second Q-operator and show that it is closely related to the inverse of the first. The multi-B\"acklund transforms generated from the Q-operator define the fusion matrices of a 2D TQFT and we derive a linear system for the solution to the quantum B\"acklund relations in terms of the TQFT fusion coefficients.Comment: 29 pages,4 figures (v3: published version